调和好的ZX和ZH演算
Well-tempered ZX and ZH Calculi
摘要：
ZX演算是一种数学工具，通过操纵实际上代表张量网络的图来表示和分析量子运算。这些网络的两个节点族是与Z旋转或X旋转交换的节点，通常分别称为“绿色节点”和“红色节点”。ZX演算的最初公式部分是由绿色和红色节点形成的代数的性质所激发的：值得注意的是，它们形成了一个双代数-但仅限于标量因子。因此，某些酉运算的图变换和符号涉及“标量小工具”，它们表示对归一化因子的贡献。我们提出的ZX演算，形成一个双代数的重整化发电机。因此，不需要标量小工具来表示最常见的酉变换，并且相应的图变换通常更简单。我们还提出了一个类似的重整化版本的ZH演算。我们获得这些结果的条件下，各种“理想化”重写是健全的分析，利用现有的介绍ZX和ZH结石。
英文摘要：
The ZX calculus is a mathematical tool to represent and analyse quantum operations by manipulating diagrams which in effect represent tensor networks. Two families of nodes of these networks are ones which commute with either Z rotations or X rotations, usually called "green nodes" and "red nodes" respectively. The original formulation of the ZX calculus was motivated in part by properties of the algebras formed by the green and red nodes: notably, that they form a bialgebra -- but only up to scalar factors. As a consequence, the diagram transformations and notation for certain unitary operations involve "scalar gadgets" which denote contributions to a normalising factor. We present renormalised generators for the ZX calculus, which form a bialgebra precisely. As a result, no scalar gadgets are required to represent the most common unitary transformations, and the corresponding diagram transformations are generally simpler. We also present a similar renormalised version of the ZH calculus. We obtain these results by an analysis of conditions under which various "idealised" rewrites are sound, leveraging the existing presentations of the ZX and ZH calculi.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
